Trigonomic Identities Etc

Reciprocal Identity (csc θ)

1 / sin θ

Reciprocal Identity (sec θ)

1 / cos θ

Reciprocal Identity (cot θ)

1 / tan θ

Quotient Identity (tan θ)

sin θ / cos θ

Quotient Identity (cot θ)

cos θ / sin θ

Pythagorean Identity (sine and cosine)

sin²θ + cos²θ = 1

Pythagorean Identity (tangent and secant)

1 + tan²θ = sec²θ

Pythagorean Identity (cotangent and cosecant)

1 + cot²θ = csc²θ

Even-Odd Identity (cos(-x))

cos x

Even-Odd Identity (sin(-x))

-sin x

Even-Odd Identity (tan(-x))

-tan x

Even-Odd Identity (sec(-x))

sec x

Even-Odd Identity (csc(-x))

-csc x

Even-Odd Identity (cot(-x))

-cot x

Co-Function Identity (sin(π/2 - x))

cos x

Co-Function Identity (cos(π/2 - x))

sin x

Co-Function Identity (tan(π/2 - x))

cot x

Co-Function Identity (csc(π/2 - x))

sec x

Co-Function Identity (sec(π/2 - x))

csc x

Co-Function Identity (cot(π/2 - x))

tan x

Sum Formula (sin(a + b))

sin a cos b + cos a sin b

Difference Formula (sin(a - b))

sin a cos b - cos a sin b

Sum Formula (cos(a + b))

cos a cos b - sin a sin b

Difference Formula (cos(a - b))

cos a cos b + sin a sin b

Sum Formula (tan(a + b))

(tan a + tan b) / (1 - tan a tan b)

Difference Formula (tan(a - b))

(tan a - tan b) / (1 + tan a tan b)

Double Angle Identity (sin 2θ)

2 sin θ cos θ

Double Angle Identity (cos 2θ - all 3 forms)

cos²θ - sin²θ OR 2cos²θ - 1 OR 1 - 2sin²θ

Double Angle Identity (tan 2θ)

(2 tan θ) / (1 - tan²θ)

Half-Angle Identity (sin(θ/2))

±√((1 - cos θ) / 2)

Half-Angle Identity (cos(θ/2))

±√((1 + cos θ) / 2)

Half-Angle Identity (tan(θ/2) - all 3 forms)

±√((1 - cos θ) / (1 + cos θ)) OR (1 - cos θ) / sin θ OR sin θ / (1 + cos θ)

Power-Reducing Formula (sin²θ)

(1 - cos 2θ) / 2

Power-Reducing Formula (cos²θ)

(1 + cos 2θ) / 2

Power-Reducing Formula (tan²θ)

(1 - cos 2θ) / (1 + cos 2θ)

Law of Sines

(sin A) / a = (sin B) / b = (sin C) / c

Area of an Oblique Triangle

½bc(sin A) OR ½ac(sin B) OR ½ab(sin C)

Law of Cosines (Standard Form - finding side a)

a² = b² + c² - 2bc(cos A)

Law of Cosines (Alternative Form - finding angle A)

cos A = (b² + c² - a²) / 2bc

Heron's Formula

Area = √(s(s-a)(s-b)(s-c)) where s = ½(a+b+c)